The Orbit Model
To determine the position and motion of a satellite in orbit based on
the data from the Two Line Elements, mathematical orbit models are
used. Two examples of orbit models are the
SGP4 orbit model and the
Kepler orbit model, which will be described closer in the following sections.
The SGP4 Orbit Model
The most used and most reliable orbit determination model is the SGP4
model. It was developed in 1970 for the use of near Earth satellites.
The higher accuracy of the SGP4 model compared with the accuracy of an
ordinary Kepler orbit model relies on the use of information, as for
example the atmospheric drag acting on the satellite, the
flatness of the earth and gravitational effects.
The data used to generate the
Two Line Elements also is based on the use of a
SGP4 model for Earth near satellites, and a SDP4 model for deep space satellites.
The Kepler Orbit Model
A less precise but much simpler orbit model is the traditional Kepler Orbit Model.
The Kepler Orbit Model described in the following sections will use the Julian Date as well
as the following parts of the
Two Line Elements: Time at Epoch, Inclination, Right Ascension of Ascending Node, Eccentricity, Argument of Perigee,
Mean Anomaly and Mean Motion.
Calculations for the Kepler Orbit Model
Time Since Epoch (tsE):
The first step is to calculate the time since
epoch tsE, which is the current time in Julian Date JD minus
the Julian Date at Epoch JDE.
tsE = JD - JDE
The Two Line Elements contain the Epoch Year and the Julian day of the year! To get the Julian date at
Epoch JDE it therefor requires some calculations.
First the Julian Date of day zero of the Epoch year given in the Two Line Elements has to be calculated. The
Julian Date of day zero of the year 2003 is equal to the Julian Date of the 31.st of December 2002
at 12 o'clock Universal Time.
The next step to calculate the Julian date at Epoch JDE will accordingly be to add the Julian Day and
fraction given in the Two Line Elements to the Julian Date of the day zero of the year.
Example:
Your Two Line Elements shows the following Epoch time set: 00131.70184970
This means that your Epoch Year is 2000 based on the first two numbers 00, and your Julian Day and
fraction is given by the remaining part: 131.70184970
With other words, you are looking for day 131.70184970 of the year 2000.
You obtain the according Julian Date the following way:
First you calculate the Julian Date of day zero of 2000 = Julian Date of the 31.st of December of 1999 at 12 o'clock
Universal time = 2451544
Accordingly you add the given day and fraction to the Julian Date you just calculated and you've got the Julian Date at Epoch:
JDE = 2451544 + 131.70184970 = 2451675.70184970
|
